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3 months ago

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which table represents viable solutions for y=5x, where x is the number of tickets sold for the school play a y is the amount of

money collected for the tickets?

1 answer:

AnnZ [12.3K]3 months ago

8 0

Given:

The equation at hand is:

$y=5x$

In this context, x represents the total tickets sold for the school play, while y indicates the total revenue generated from ticket sales.

To find:

The appropriate table of values from the provided options.

Solution:

It's clear that both the number of tickets and the revenue collected cannot be negative, which means that options A and B are not viable.

We have:

$y=5x$

For $x=0$ ,

$y=5(0)$

$y=0$

For $x=10$ ,

$y=5(10)$

$y=50$

For $x=51$ ,

$y=5(51)$

$y=255$

For $x=400$ ,

$y=5(400)$

$y=2000$

In option C, the ordered pairs (0,0), (10,50), (51,255), (400,2000) are present in the table. Thus, option C is the correct choice.

For $x=65$

$y=5(65)$

$y=325$

As the ordered pair (65,350) does not fulfill the requirements of the equation, thus option D is incorrect.

Consequently, the right option is C.

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2 months ago

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Answer:

Part A. At least 6 hours

Part B. In less than 2.5 hours, Elijah will fall behind Mercedes

Part C. In over 2.5 hours, Elijah will lead Aubrey

Step-by-step explanation:

D = distance

v = speed

t = time

Formula connecting D, v, and t:

$D=v\cdot t$

Part A.

Steve's speed: $v=3.5\ mph$

Distance: a minimum of 21 miles

Time: unknown, so

$3.5\cdot t\ge 21\\ \\35t\ge 210\ [\text{Multiplied by 10}]\\ \\t\ge \dfrac{210}{35}\\ \\t\ge \dfrac{30}{5}\\ \\t\ge 6$

It would require Steve a minimum of 6 hours to traverse at least 21 miles on Day 1.

Part B.

Mercedes's speed: $v_M=2.4\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Mercedes's Distance walked: $D_M$ miles

Time: x hours

Mercedes is 2 miles ahead, therefore

$D_E=3.2x\\ \\D_M=2.4x+2$

Elijah will trail behind until

$D_E$

In 2.5 hours, Elijah will close the gap on Mercedes, and in less than 2.5 hours, Elijah will trail behind her.

Part C.

Aubrey's speed: $v_M=3\ mph$

Elijah's speed: $v_E=3.2\ mph$

Elijah's Distance walked: $D_E$ miles

Aubrey's Distance walked: $D_A$ miles

Time: x hours

At the beginning of Day 3, Elijah starts from Mile 42, while Aubrey begins at Mile 42.5.

$D_E=42+3.2x\\ \\D_A=42.5+3x$

Elijah will be ahead of Aubrey when

$D_E>D_A\\ \\42+3.2x> 42.5+3x\\ \\3.2x-3x>42.5-42\\ \\0.2x>0.5\\ \\2x>5\ [\text{Multiplied by 10}]\\ \\x>\dfrac{5}{2}\\ \\x>2.5\ hours$

In 2.5 hours, Elijah will surpass Aubrey, and after more than 2.5 hours, Elijah will outpace Aubrey.

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2 months ago

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